Paul Erdős and László Lovász established by means of an example that there exists a maximal intersecting family of k-sets with blocks, where e is the base of natural logarithm. László Lovász conjectured that their example is best known example which has the maximum number of blocks. Later it was disproved. But the quest for such examples remain valid till this date. In this note we compute the transversal size of a certain series of intersecting families of k-sets, which is constructed over the Cyclic graph. It helps to provide an example of maximal intersecting family of k-sets with so many blocks and to present two worthwhile examples which disprove two special cases of one of the conjectures of Frankl et al.
